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# Learning Simple Auctions

*29th Annual Conference on Learning Theory*, PMLR 49:1298-1318, 2016.

#### Abstract

We present a general framework for proving polynomial sample complexity bounds for the problem of learning from samples the best auction in a class of “simple” auctions. Our framework captures the most prominent examples of “simple” auctions, including anonymous and non-anonymous item and bundle pricings, with either a single or multiple buyers. The first step of the framework is to show that the set of auction allocation rules have a low-dimensional representation. The second step shows that, across the subset of auctions that share the same allocations on a given set of samples, the auction revenue varies in a low-dimensional way. Our results effectively imply that whenever it is possible to compute a near-optimal simple auction with a known prior, it is also possible to compute such an auction with an unknown prior, given a polynomial number of samples.